Abstract
Let (A,*) be an involutive ring. Then the groups Sl *(2, A), are a non commutative version of the special linear groups Sl(2, F) defined over a field F. In particular, if A = M(n, F) and * is transposition, then Sl *(2, M n (F)) = Sp(2n, F). The above groups were defined by Pantoja and Soto-Andrade, and a set of generators for the group SSl *(2, A) (which is either Sl *(2, A) or a index 2 subgroup of Sl *(2, A)) was given in the case when A is an artinian ring. In this paper, we prove that the mentioned generators provide a presentation of the mentioned groups in the case of simple artinian rings.
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Partially supported by FONDECYT project 1030907 and Pontificia Universidad Católica de Valparaíso
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Pantoja, J. A presentation of the group Sl * (2, A), A a simple artinian ring with involution. manuscripta math. 121, 97–104 (2006). https://doi.org/10.1007/s00229-006-0027-5
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DOI: https://doi.org/10.1007/s00229-006-0027-5